Automorphic Forms on Adele Groups

This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and systematically develops explicit consequences and connections with the classical theory. The underlying theme is the decomposition of the regular representation of the adele group of GL(2). A detailed proof of the celebrated trace formula of Selberg is included, with a discussion of the possible range of applicability of this formula. Throughout the work the author emphasizes new examples and problems that remain open within the general theory.

TABLE OF CONTENTS: 1. The Classical Theory 2. Automorphic Forms and the Decomposition of L2(PSL(2,R) 3. Automorphic Forms as Functions on the Adele Group of GL(2) 4. The Representations of GL(2) over Local and Global Fields 5. Cusp Forms and Representations of the Adele Group of GL(2) 6. Hecke Theory for GL(2) 7. The Construction of a Special Class of Automorphic Forms 8. Eisenstein Series and the Continuous Spectrum 9. The Trace Formula for GL(2) 10. Automorphic Forms on a Quaternion Algebr?

About the author

Stephen S. Gelbart

Summary

The subject matter of these Notes is the interplay between the theory of automorphic forms and group representations. One goal is to interpret some recent developments in this area, most significantly the theory of Jacquet-Langlands, working out, whenever possible, explicit consequences and connections with the classical theory. Another goal is to

Product details

• Authors: Stephen Gelbart, Stephen S. Gelbart, Gelbart Stephen S.
• Assisted by: Elias Gelbart (Editor), Phillip Griffiths (Editor), John N. Mather (Editor)
• Publisher: University Presses
• Languages: English
• Product format: Paperback / Softback
• Released: 21.03.1975
• EAN: 9780691081564
• ISBN: 978-0-691-08156-4
• No. of pages: 227
• Weight: 397 g
• Series: Annals of Mathematics Studies; Annals of Mathematics Studies
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; Algebra, MATHEMATICS / Group Theory, MATHEMATICS / Algebra / General, Groups & group theory, Groups and group theory